Risk minimization with incomplete information in a model for high-frequency data (Q2707144)

This paper is devoted to the risk-minimizing hedging-strategies for derivatives with incomplete information, taking into account high frequency data. Since diffusion models are of limited use in modeling tick-by-tick data for asset prices, the author proposes an alternative model, where asset prices follow a marked point process with stochastic jump-intensity, which depends on some unobservable state-variable process. This models the fact that real markets exhibit random fluctuations of market activity, which are related to fluctuations in the amount of incoming news. In his approach, the author makes use of the criterion of risk minimization proposed by \textit{H. Föllmer} and \textit{D. Sondermann} [Contributions to mathematical economics, Hon. G. Debreu, 206-223 (1986; Zbl 0663.90006)]. Due to the incomplete information, the solution of the problem of computing the hedge strategy consists in two steps: First, a risk-minimizing strategy is computed for a fictitious agent, who is informed about the jump-intensity (full-information case). In the second step, a projection result by \textit{M. Schweizer} [Math. Finance 4, 327-342 (1994; Zbl 0884.90051)] is used to obtain a risk-minimizing for the agent, who is restricted to observing the asset prize process (incomplete information case). The computation of the strategy leads to the problem of computing certain conditional expectations, which has received some attention in the literature on nonlinear filtering.